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Mike Boyle, Jerome Buzzi, Ricardo Gmez

Almost isomorphism for countable state Markov shifts

Countable state Markov shifts are a natural generalization of the well-known subshifts of finite type. They are the subject of current research both for their own sake and as models for smooth dynamical systems. In this paper, we investigate their almost isomorphism and entropy conjugacy and obtain a complete classification for the especially important class of strongly positive recurrent Markov shifts. This gives a complete classification up to entropy-conjugacy of the natural extensions of smooth entropy-expanding maps, e.g., C^∞ smooth interval maps with non-zero topological entropy.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2006, 03/2006
Pages: 23 - 47

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